David measures a line to be 7.6ft long. If the actual measurement is 8ft, find David's relative error to the nearest thousandth. Answer:

Understand relative error: Understand the concept of relative error. Relative error is the absolute error divided by the actual measurement, often expressed as a percentage or a decimal. In this case, we need to find the absolute error first, which is the difference between the measured value and the actual value.Calculate absolute error: Calculate the absolute error. Absolute error = |Measured Value - Actual Value| Absolute error = |7.6ft - 8ft| Absolute error = |-0.4ft| Absolute error = 0.4ftCalculate relative error: Calculate the relative error. Relative error = (Absolute Error / Actual Value) Relative error = (0.4ft / 8ft) Relative error = 0.05Convert to nearest thousandth: Convert the relative error to the nearest thousandth. To express the relative error to the nearest thousandth, we keep three decimal places. Relative error = 0.050

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Grade 7

Percent error: word problems

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Q. David measures a line to be

7.6 \mathrm{ft}

long. If the actual measurement is

8 \mathrm{ft}

, find David's relative error to the nearest thousandth.

\newline

Answer:

Understand relative error: Understand the concept of relative error. $\newline$ Relative error is the absolute error divided by the actual measurement, often expressed as a percentage or a decimal. In this case, we need to find the absolute error first, which is the difference between the measured value and the actual value.
Calculate absolute error: Calculate the absolute error. $\newline$ Absolute error = $|\text{Measured Value} - \text{Actual Value}|$ $\newline$ Absolute error = $|7.6\text{ft} - 8\text{ft}|$ $\newline$ Absolute error = $|-0.4\text{ft}|$ $\newline$ Absolute error = $0.4\text{ft}$
Calculate relative error: Calculate the relative error. $\newline$ Relative error = $(\text{Absolute Error} / \text{Actual Value})$ $\newline$ Relative error = $(0.4\,\text{ft} / 8\,\text{ft})$ $\newline$ Relative error = $0.05$
Convert to nearest thousandth: Convert the relative error to the nearest thousandth. $\newline$ To express the relative error to the nearest thousandth, we keep three decimal places. $\newline$ Relative error = $0.050$